You’re in a spanking new home where ceiling fans have an on/off pull chain. One day you pull that chain, but nothing happens. So you figure it’s because of a temporary power cut. Unfortunately, you have to leave immediately for some sordid little affair in another city and won’t be back for a few days.
What you do know, however, is that the fan was in the “off” position before you pulled the chain, and that pulling it successively will only cycle it through its remaining settings (“off,” “high,” “medium,” etc.). But you have no idea how many settings there are, though you know there can’t be more than four. How can you make sure the fan will be in the “off” position when power is restored? (No, you can’t cut it off at the mains.)
(The problem was: “You tell your friend a certain woman’s mother-in-law and your mother-in-law are, in some order, mother and daughter. Your friend says this could be if she’s your daughter-in-law. True, but you give two more solutions?”)
Too many in laws by law! Two other solutions are: (1) She is my sister-in-law’s daughter-in-law. In which case her mother-in-law is the daughter of my mother-in-law; (2) She is my wife’s aunt, wife of my mother-in-law’s brother. In which case her mother-in-law is the mother of my mother-in-law. -- -- Raghavendra Rao Hebbani, email@example.com
So, we have me and a woman I and my friend passed during our walk in the park and mothers-in-law of both to begin with. And since the relationship between the two mothers-in-law is not clearly given, my mother-in-law can be the mother or daughter of the mother-in-law of the woman. Consider the case where my mother-in-law is the mother of the other mother-in-law. So, the other mother-in-law will be either my wife or her sister. In the former case, the woman in the problem will be our daughter-in-law and in the latter case she will be the daughter-in-law of my sister-in-law; wife’s sister. In the case where my mother-in-law is the daughter of the other mother-in-law, she would be the grandmother of my wife. Her daughter-in-law -- ie, her son’s wife -- would be my wife’s sister-in-law. Therefore, the woman I and my friend passed during our walk may be (a) my daughter-in-law, (b) my wife’s sister’s daughter-in-law or (c) my wife’s sister-in-law. -- Balagopalan Nair K, firstname.lastname@example.org
There should be a law against such problems! Anyway, as mentioned, the woman can be the man’s daughter-in-law, because his wife is the daughter of his mother-in-law. Or the woman can be the man’s wife’s aunt (his mother-in-law’s brother’s wife), because his mother-in-law is the daughter of her own brother’s wife’s mother-in-law. Or the woman can be the wife of the man’s nephew (the wife of his wife’s sister’s son), because his wife is the daughter of his mother-in-law. -- Dhruv Narayan, email@example.com
(The second one was: “So these newlyweds want four kids with an exact mix of sexes. Assuming the chances are equal, what’s more likely: two girls and two boys or three of one and one of the other?”)
Three of one and one of the other is more likely (probability 0.5) than two of each (probability 0.375). Idea gleaned from any parody of the rhyme? -- J Vaseekhar Manuel, firstname.lastname@example.org
There are 2*2*2*2 = 16 ways in which to arrange the sequence of four deliveries as each delivery can be a boy or a girl. So, each sequence has 1/16 chance. There are 4C3 ways of getting three boys and one girl. Similarly, there are 4C3 ways of getting three girls and one boy. There are 4C2 ways of getting two boys and two girls. So, the probability of two boys and two girls is (4C2)(1/16) = 6/16. Probability of three of one and one of the other is (4C3+4C3)(1/16) = 8/16. The three of one and one of another is more likely. It follows binomial distribution. -- Abhay Prakash, email@example.com
BUT GOOGLE THIS NOW
Here are eight clues which are easy to Google but once you have the answers there’s something else you have to do to make them belong to a certain group. (1) Unfortunate second wife of Henry VIII; (2) This killed Moaning Myrtle; (3) The Scourge of God; (4) Winston Smith’s dreary country; (5) Birch film or attractive rose; (6) Romeo’s loyal, peacemaker cousin; (7) King Arthur’s island paradise; (8) Supreme and powerful Norse god.
Sharma is a scriptwriter and former editor of Science Today magazine.